Odd Snake Hook Tool Glitch?
That's actually not a glitch. As weird as it looks, the Snake Hook tool is behaving exactly like it should in your case.

To get the tool working as you want it too, your object needs more geometry (more faces/vertices). Sculpting by default only modifies the vertices that your object has. In order to get the tool to pull out a tentacle like shape (like what is shown on the tool icon) you need some way of adding more vertices to your mesh. Currently the brush only affect the dozen or so vertices that are under it when you click. This is not nearly enough to create the shape shown by the brush icon. There are 3 main ways to add more vertices:


Add more vertices manually: This is probably not what you want to do in your case, but one of the ways to add more vertices is to simply add them in edit mode. You could use the loop cut tool (Ctrl+R) or subdivide(W) or some other tool. The reason you dont want to do it this way in your case is because for your object one of the next two ways will be better.
Multiresolution Modifier: The multiresolution modifier works very similar to the subdivision surface modifier in that it subdivides each face (splits it into 4 smaller faces) and then smooths the result. The difference is that the small faces generated by the multires modifier are sculptable, where as they are not for the subsurf modifier. To add a multires modifier, select your object and navigate to the modifier tab in the properties panel (the little wrench in the row of icons near the top left of your screen. Click the add modifier button and select Multiresolution from the Generate column (about halfway down). Then in the modifier option click subdivide as many times as you need to get it as smooth as you want. Just be careful as this modifier can generate a lot of vertices and make blender run slower.
Dynamic Topology: This will probably be what you want to do to get the results you are looking for. In sculpt mode, in the toolbar on the left there will be a panel titled Dyntopo (short for Dynamic Topology). Checking this option will make the Snake Hook tool generate new vertices only where it need them. You may want to adjust the detail size to make it smoother if need be. I would recommend looking up a tutorial that explains sculpting as it will be more thorough than I am here.


If you are new to Blender you are probably going to run into a lot more problems like this, as Blender is sometimes a bit unconventional in how it goes about certain things. There are many good introductory tutorials that can get you up to speed. CG Cookie and BlenderGuru both have excellent introductory series that can help you get started.